It occurs to me that I might be interested in starting a new group altogether or at least pitch out an interest check in a new group idea. And it might not be a great idea to try to pitch that in my old group thread. Would it be okay to pitch an interest check on this new group even if it used a similar game mechanic as the previous one? Different game idea, but the same system (a la D&D, d20, etc).

Perfectly fine to put up a new thread to pitch a new interest. The only restrictions are the general ones for all RP requests - the fact that you had a previous interest thread (similar or not) is irrelevant.

Gotcha. I figured it would be okay to post up "Hey, I got an idea to take this system from my current game and make THIS with it". But I didn't want to assume, and I wanted to be considerate of fellow members. Group RP traffic isn't quite as "competitive" as Single Requests are, but I still like to keep the "bumping" policy, it's intention and stuff like that in mind.